The present invention relates to a method and an apparatus for waveform equalization, and in particular to an equalization method and an equalization apparatus for transmitting digital signals or recording/ reproducing digital signals onto/from a recording medium.
When digital signals are to be recorded onto/ reproduced from a VTR or the like or are to be transmitted via a telephone line or the like, these medium have frequency cutoff characteristics. In some cases, therefore, digital codes crumble so as to cause interference between digital codes and it becomes difficult to discriminate between a logic "1" and a logic "0" of the digital signal.
When necessary digital signals are to be discriminated and reproduced from those waveforms, therefore, it is necessary to perform waveform compensation so that the discrimination may be performed without making an error.
By passing one waveform similar to a rectangular impulse having a time width T', for example, through the above described medium, a waveform as shown in FIG. 4B is obtained. Such a waveform is herein referred to as isolated impulse response waveform (hereafter simply abbreviated to impulse respons waveform). It is now assumed that the time width T'means a clock period of the MFM (Modified Frequency Modulation) scheme which is one of digital modulation schemes. And it is further assumed that the clock period T' is related to a bit period T of the digital data before modulation by relation T'=T/2 as described later. As means for applying the above described waveform compensation to the impulse response waveform as shown in FIG. 4B to obtain a so-called equalized waveform as shown in FIG. 4C, it is heretofore known to use a transversal filter comprising a delay circuit and an attenuator as shown in FIG. 4A (as described in "PCM Tsushin no Shinpo --"Progress in PCM Communication"written by Hiroshi Inose and Hiroshi Miyazawa and published by Sanpo, for example). In this equalization method, delay elements are connected in series. (Connection points between delay elements are referred to as taps. A transversal filter having three taps is illustrated in FIG. 4A.) In the above described equalization method, the weighted sum of outputs of respective taps of the serially connected delay elements (i.e., the sum of the product of respective outputs with attenuation coefficients) is used to eliminate intersymbol interference caused in the recording and reproducing system in principle.
The summary of the waveform equalization method using a transversal filter will now be described by referring to time charts of FIGS. 5A to 5C.
FIG. 5A shbws an ideal impulse response waveform having no intersymbol interference. This signal is denoted by i(t). If the high frequency response is deteriorated, the signal i(t) is typically changed to a signal S(t) as shown in FIG. 5B. "In FIG. 5B, a signal amplitude of S(t) at a time =T' is shown by S(T'). In other words, a signal which should originally become S(nT') =0 at t =nT'(where n is an integer, and n.noteq.0) has an amount S(nT') of intersymbol interference. If noises are added to this signal, errors tend to be caused in that portion.
Such intersymbol interference is removed as follows. If the above described S(t) is inputted to the circuit of FIG. 4A, S(t) is typically delayed by Td in a delay circuit as far as a central tap. Accordingly, the output signal of the central tap is represented as
Sd(t) =S(t-Td).
Signal sums corresponding to the amounts of intersymbol interference of Sd(t) at t =Td.+-.T' are derived as sums of output signals from taps other than the central tap. These signal sums are subtracted from the signal obtained at the central tap to make output results at a t =Td.+-.T' equal to zero. Amounts of intersymbol interference at these points are thus cancelled. As the output signals for producing these signal sums, an output signal obtained by passing the signal appearing at the input tap through an attenuator and an output signal obtained by passing the signal appearing at the input tap through delay circuits 11 and 12 respectively for delaying an input signal by T'successively and an attenuator 15 are used in FIG. 4A. The output signals of other taps are two signal waveforms as shown in FIG. 5D which differ in phase by T' with respect to the output signal Sd(t) of the central tap. The output signals of other taps are represented as
p(t) =a.multidot.Sd t.+-.T')
where a is an attenuation coefficient. The right side of the above described equation are elements of the above described weighted sum, and a represents a weighting coefficient.
If the output Sd(t) of the central tap as shown in FIG. 4A is supplied to a "+" terminal of an adder 16 and the outputs of other taps are respectively supplied to "-" terminals of the adder 16 to perform addition, the output So(t) of the adder 16 is given by EQU Sd(t) =So(t) -p(t)
The above described a is so defined that So(t) provides null outputs at t =Td.+-.T' as shown in FIG. 5E. In other words, the signal So(t) having no intersymbol interference as shown in FIG. 5E is obtained. The right side (Sd(t) -p(t)) of the equation shown above means the above described weighted sum.
The MFM signal which is one of the subjects of waveform equalization of the present invention is used in many apparatuses because the difference between the maximum and the minimum of the signal inversion interval is small and the magnetization inversion is not often performed. FIG. 6A shows an example of an NRZ signal before modulation. FIG. 6B shows an waveform diagram after MFM modulation. In the MFM modulation scheme, a logic "1" of the input signal is associated with inversion of polarity at a center of a bit period, and a logic "0" is associated with noninversion of polarity. If two logic "0" s are consequtive, however, the polarity is inverted on a boundary between bit periods.
As evident from the foregoing description, inversion intervals of the MFM signal become T, 1.5T and 2T. Accordingly, the clock frequency must be twice the frequency of the NRZ signal. In view of this clock timing, the inversion interval becomes 2T', 3T' and 4T' with respect to the clock period T', where T'=T/2. Assuming that intersymbol interference is caused on an MFM signal having an inversion interval of 2T', i.e., on an MFM signal comprising two consecutive bits of logic 1's, as an example, the waveform equalization method will now be described.
A signal having two consecutive bits of logic 1's has a rectangular waveform as shown in FIG. 7A. This is considered to be two consecutive rectangular waveforms, each of which corresponds to a single bit. When this signal is recorded and reproduced by a VTR or the like and its frequency characteristics are deteriorated, rectangular waveforms which are input signals become isolated waves having spread skirts, resulting in the lowered amplitude. In this case, however, two consecutive isolated waves overlap each other, resulting in a waveform as shown in FIG. 7B. That is to say, the amount f(T') of intersymbol interference overlaps with the peak of each isolated wave at T', resulting in a signal amplitude decreased by f(T').
When the conventional waveform equalization method is used, however, the reproduced signal as shown in FIG. 7B is restored to a correct signal having no intersymbol interference, resulting in a rather reduced signal amplitude as shown in FIG. 7C. When two waveforms shown by real lines in FIG. 7B are respectively equalized in accordance with the method show in FIGS. 5B -5E, two waveforms shown by real lines in FIG. 7C are obtained and as a result the amplitude doubled by these two waveforms is reduced from a value shown by a dotted line in FIG. 7B to a value shown by a dotted line in FIG. 7C. In other words, a digital modulated signal comprising a plurality of consecutive isolated waves, the signal amplitude is reduced by an amount corresponding to the removed intersymbol interference, resulting in raised probability of occurrence of code errors.